Subgroups — C₅×#3555 #10619340

Order 640.

910 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#563	C₂	1	4	yes	maximal, complemented
2	C₅×Q₈²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#557	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#557	C₂	1	2	yes	maximal, complemented
5	C₅×#556	C₂	1	2	yes	maximal, complemented
6	C₅×#556	C₂	1	2	yes	maximal, complemented
7	C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#552	C₂	1	2	yes	maximal, complemented
10	C₅×#544	C₂	1	2	yes	maximal, complemented
11	C₅×#542	C₂	1	2	yes	maximal
12	C₅×#541	C₂	1	2	yes	maximal, complemented
13	C₅×#541	C₂	1	2	yes	maximal, complemented
14	C₅×#541	C₂	1	4	yes	maximal, complemented
15	C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#529	C₂	1	1	yes	maximal, characteristic
18	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₅×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₅×C₄⋊Q₈	C₂²	1	4	yes	—
24	C₅×C₄⋊Q₈	C₂²	1	2	yes	—
25	C₅×C₄⋊Q₈	C₂²	1	2	yes	—
26	C₅×C₄⋊Q₈	C₂²	1	4	yes	—
27	C₅×#126	C₂²	1	2	yes	—
28	C₅×#126	C₂²	1	4	yes	—
29	C₅×#126	C₂²	1	4	yes	—
30	C₅×#126	C₂²	1	4	yes	—
31	C₅×#126	C₂²	1	4	yes	—
32	C₅×#126	C₂²	1	4	yes	—
33	C₅×#126	C₂²	1	4	yes	—
34	C₅×#125	C₂²	1	1	yes	characteristic
35	C₅×#125	C₂²	1	2	yes	—
36	C₅×#125	C₂²	1	2	yes	—
37	C₅×#125	C₂²	1	4	yes	—
38	C₅×#125	C₂²	1	4	yes	—
39	C₅×#125	C₂²	1	4	yes	—
40	C₅×#125	C₂²	1	2	yes	—
41	C₅×#125	C₂²	1	4	yes	—
42	C₅×#125	C₂²	1	4	yes	—
43	C₅×#125	C₂²	1	2	yes	—
44	C₅×#124	C₂²	1	1	yes	characteristic
45	C₅×#124	C₂²	1	2	yes	—
46	C₅×#124	C₂²	1	4	yes	—
47	C₅×#123	C₂²	1	2	yes	—
48	C₅×#123	C₂²	1	4	yes	—
49	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
50	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
52	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
53	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
54	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
55	C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
56	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
57	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
58	C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
59	C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
60	C₅×#121	C₂²	1	1	yes	characteristic
61	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
62	C₄×C₅×Q₈	C₂²	1	2	yes	—
63	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
64	C₄×C₅×Q₈	C₂²	1	2	yes	—
65	C₄×C₅×Q₈	C₂²	1	2	yes	—
66	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
67	C₄×C₅×Q₈	C₂²	1	2	yes	—
68	C₄×C₅×Q₈	C₂²	1	4	yes	—
69	C₄×C₅×Q₈	C₂²	1	2	yes	—
70	C₄×C₅×Q₈	C₂²	1	2	yes	—
71	C₄×C₅×Q₈	C₂²	1	2	yes	—
72	C₄×C₅×Q₈	C₂²	1	2	yes	—
73	C₄×C₅×D₄	C₂²	1	2	yes	—
74	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
75	C₄×C₅×D₄	C₂²	1	2	yes	—
76	C₅×#117	C₂²	1	2	yes	—
77	C₅×#117	C₂²	1	2	yes	—
78	C₅×#117	C₂²	1	2	yes	—
79	C₅×#117	C₂²	1	4	yes	—
80	C₅×#117	C₂²	1	2	yes	—
81	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
82	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
83	#3555	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
85	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
87	C₂×C₅×Q₈	C₂³	1	2	yes	—
88	C₂×C₅×Q₈	C₂³	1	2	yes	—
89	C₂×C₅×Q₈	C₂³	1	2	yes	—
90	C₂×C₅×Q₈	C₂³	1	4	yes	—
91	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
92	C₂×C₅×D₄	C₂³	1	2	yes	—
93	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂³	1	2	yes	—
96	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂³	1	4	yes	—
98	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₅×C₄⋊C₄	C₂³	1	2	yes	—
100	C₅×C₄⋊C₄	C₂³	1	4	yes	—
101	C₅×C₄⋊C₄	C₂³	1	2	yes	—
102	C₅×C₄⋊C₄	C₂³	1	2	yes	—
103	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₅×C₄⋊C₄	C₂³	1	2	yes	—
105	C₅×C₄⋊C₄	C₂³	1	2	yes	—
106	C₅×C₄⋊C₄	C₂³	1	4	yes	—
107	C₅×C₄⋊C₄	C₂³	1	2	yes	—
108	C₅×C₄⋊C₄	C₂³	1	2	yes	—
109	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₅×C₄⋊C₄	C₂³	1	2	yes	—
111	C₅×C₄⋊C₄	C₂³	1	2	yes	—
112	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₅×C₄⋊C₄	C₂³	1	2	yes	—
114	C₅×C₄⋊C₄	C₂³	1	2	yes	—
115	C₅×C₄⋊C₄	C₂³	1	4	yes	—
116	C₅×C₄⋊C₄	C₂³	1	4	yes	—
117	C₅×C₄⋊C₄	C₂³	1	4	yes	—
118	C₅×C₄⋊C₄	C₂³	1	4	yes	—
119	C₅×C₄⋊C₄	C₂³	1	4	yes	—
120	C₅×C₄⋊C₄	C₂³	1	2	yes	—
121	C₅×C₄⋊C₄	C₂³	1	2	yes	—
122	C₅×C₄⋊C₄	C₂³	1	2	yes	—
123	C₅×C₄⋊C₄	C₂³	1	4	yes	—
124	C₅×C₄⋊C₄	C₂³	1	2	yes	—
125	C₅×C₄⋊C₄	C₂³	1	4	yes	—
126	C₅×C₄⋊C₄	C₂³	1	4	yes	—
127	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
136	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₄²×C₅	C₂³	1	1	yes	characteristic
139	C₄²×C₅	C₂³	1	1	yes	characteristic
140	C₄²×C₅	C₂³	1	1	yes	characteristic
141	C₄²×C₅	C₂³	1	1	yes	characteristic
142	C₄²×C₅	C₂³	1	4	yes	—
143	C₄²×C₅	C₂³	1	2	yes	—
144	C₄²×C₅	C₂³	1	2	yes	—
145	C₄²×C₅	C₂³	1	2	yes	—
146	C₄²×C₅	C₂³	1	4	yes	—
147	C₄²×C₅	C₂³	1	4	yes	—
148	C₄²×C₅	C₂³	1	4	yes	—
149	#563	C₂×C₅	1	4	yes	complemented
150	Q₈²	C₂×C₅	1	1	yes	characteristic, complemented
151	#557	C₂×C₅	1	1	yes	characteristic, complemented
152	#557	C₂×C₅	1	2	yes	complemented
153	#556	C₂×C₅	1	2	yes	complemented
154	#556	C₂×C₅	1	2	yes	complemented
155	#556	C₂×C₅	1	1	yes	characteristic, complemented
156	#554	C₂×C₅	1	1	yes	characteristic, complemented
157	#552	C₂×C₅	1	2	yes	complemented
158	#544	C₂×C₅	1	2	yes	complemented
159	#542	C₂×C₅	1	2	yes	—
160	#541	C₂×C₅	1	2	yes	complemented
161	#541	C₂×C₅	1	2	yes	complemented
162	#541	C₂×C₅	1	4	yes	complemented
163	#533	C₂×C₅	1	1	yes	characteristic, complemented
164	#533	C₂×C₅	1	1	yes	characteristic, complemented
165	#529	C₂×C₅	1	1	yes	characteristic
166	C₂³×C₅	C₂⁴	1	1	yes	characteristic
167	C₂³×C₅	C₂⁴	1	2	yes	—
168	C₅×Q₈	—	2	2	no	—
169	C₅×Q₈	—	2	2	no	—
170	C₅×Q₈	—	2	2	no	—
171	C₅×Q₈	—	2	4	no	—
172	C₅×Q₈	—	4	2	no	—
173	C₅×Q₈	—	4	2	no	—
174	C₅×Q₈	—	4	4	no	—
175	C₅×D₄	—	2	2	no	—
176	C₅×D₄	—	4	2	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	—	2	4	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	4	4	no	—
181	C₂×C₄×C₅	—	4	1	no	—
182	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂⁴	1	4	yes	—
184	C₂×C₄×C₅	C₂⁴	1	2	yes	—
185	C₂×C₄×C₅	C₂⁴	1	2	yes	—
186	C₂×C₄×C₅	C₂⁴	1	2	yes	—
187	C₂×C₄×C₅	C₂⁴	1	2	yes	—
188	C₂×C₄×C₅	C₂⁴	1	2	yes	—
189	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂⁴	1	2	yes	—
191	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂⁴	1	4	yes	—
194	C₂×C₄×C₅	C₂⁴	1	2	yes	—
195	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
197	C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
198	C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
199	C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
200	C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
201	C₄⋊Q₈	C₂²×C₅	1	2	yes	—
202	C₄⋊Q₈	C₂²×C₅	1	4	yes	—
203	C₄⋊Q₈	C₂²×C₅	1	2	yes	—
204	C₄⋊Q₈	C₂²×C₅	1	2	yes	—
205	C₄⋊Q₈	C₂²×C₅	1	4	yes	—
206	#126	C₂²×C₅	1	2	yes	—
207	#126	C₂²×C₅	1	4	yes	—
208	#126	C₂²×C₅	1	4	yes	—
209	#126	C₂²×C₅	1	4	yes	—
210	#126	C₂²×C₅	1	4	yes	—
211	#126	C₂²×C₅	1	4	yes	—
212	#126	C₂²×C₅	1	4	yes	—
213	#125	C₂²×C₅	1	1	yes	characteristic
214	#125	C₂²×C₅	1	2	yes	—
215	#125	C₂²×C₅	1	2	yes	—
216	#125	C₂²×C₅	1	4	yes	—
217	#125	C₂²×C₅	1	4	yes	—
218	#125	C₂²×C₅	1	4	yes	—
219	#125	C₂²×C₅	1	2	yes	—
220	#125	C₂²×C₅	1	4	yes	—
221	#125	C₂²×C₅	1	4	yes	—
222	#125	C₂²×C₅	1	2	yes	—
223	#124	C₂²×C₅	1	1	yes	characteristic
224	#124	C₂²×C₅	1	2	yes	—
225	#124	C₂²×C₅	1	4	yes	—
226	#123	C₂²×C₅	1	2	yes	—
227	#123	C₂²×C₅	1	4	yes	—
228	C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
229	C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
230	C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
231	C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
232	C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
233	C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
234	C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
235	C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
236	C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
237	C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
238	C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
239	#121	C₂²×C₅	1	1	yes	characteristic
240	C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
241	C₄×Q₈	C₂²×C₅	1	2	yes	—
242	C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
243	C₄×Q₈	C₂²×C₅	1	2	yes	—
244	C₄×Q₈	C₂²×C₅	1	2	yes	—
245	C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
246	C₄×Q₈	C₂²×C₅	1	2	yes	—
247	C₄×Q₈	C₂²×C₅	1	4	yes	—
248	C₄×Q₈	C₂²×C₅	1	2	yes	—
249	C₄×Q₈	C₂²×C₅	1	2	yes	—
250	C₄×Q₈	C₂²×C₅	1	2	yes	—
251	C₄×Q₈	C₂²×C₅	1	2	yes	—
252	C₄×D₄	C₂²×C₅	1	2	yes	—
253	C₄×D₄	C₂²×C₅	1	1	yes	characteristic
254	C₄×D₄	C₂²×C₅	1	2	yes	—
255	#117	C₂²×C₅	1	2	yes	—
256	#117	C₂²×C₅	1	2	yes	—
257	#117	C₂²×C₅	1	2	yes	—
258	#117	C₂²×C₅	1	4	yes	—
259	#117	C₂²×C₅	1	2	yes	—
260	C₂×C₄⋊C₄	C₂²×C₅	1	2	yes	—
261	C₂×C₄²	C₂²×C₅	1	1	yes	characteristic
262	C₂²×C₅	—	2	1	no	—
263	C₂²×C₅	—	2	1	no	—
264	C₂²×C₅	—	2	2	no	—
265	C₂²×C₅	—	2	2	no	—
266	C₂²×C₅	—	2	2	no	—
267	C₂²×C₅	—	2	1	no	—
268	C₂²×C₅	C₂⁵	1	1	yes	characteristic
269	C₄×C₅	—	2	1	no	—
270	C₄×C₅	—	2	2	no	—
271	C₄×C₅	—	2	1	no	—
272	C₄×C₅	—	2	2	no	—
273	C₄×C₅	—	2	2	no	—
274	C₄×C₅	—	2	4	no	—
275	C₄×C₅	—	2	2	no	—
276	C₄×C₅	—	2	2	no	—
277	C₄×C₅	—	2	4	no	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	2	2	no	—
281	C₄×C₅	—	2	2	no	—
282	C₄×C₅	2₋¹⁺⁴	1	2	yes	—
283	C₄×C₅	2₋¹⁺⁴	1	2	yes	—
284	C₂×Q₈	C₂³×C₅	1	1	yes	characteristic
285	C₂×Q₈	C₂³×C₅	1	1	yes	characteristic
286	C₂×Q₈	C₂³×C₅	1	1	yes	characteristic
287	C₂×Q₈	C₂³×C₅	1	2	yes	—
288	C₂×Q₈	C₂³×C₅	1	2	yes	—
289	C₂×Q₈	C₂³×C₅	1	2	yes	—
290	C₂×Q₈	C₂³×C₅	1	4	yes	—
291	C₂×D₄	C₂³×C₅	1	1	yes	characteristic
292	C₂×D₄	C₂³×C₅	1	2	yes	—
293	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
294	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
295	C₂²×C₄	C₂³×C₅	1	2	yes	—
296	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₅	1	4	yes	—
298	C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
299	C₄⋊C₄	C₂³×C₅	1	2	yes	—
300	C₄⋊C₄	C₂³×C₅	1	4	yes	—
301	C₄⋊C₄	C₂³×C₅	1	2	yes	—
302	C₄⋊C₄	C₂³×C₅	1	2	yes	—
303	C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
304	C₄⋊C₄	C₂³×C₅	1	2	yes	—
305	C₄⋊C₄	C₂³×C₅	1	2	yes	—
306	C₄⋊C₄	C₂³×C₅	1	4	yes	—
307	C₄⋊C₄	C₂³×C₅	1	2	yes	—
308	C₄⋊C₄	C₂³×C₅	1	2	yes	—
309	C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
310	C₄⋊C₄	C₂³×C₅	1	2	yes	—
311	C₄⋊C₄	C₂³×C₅	1	2	yes	—
312	C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
313	C₄⋊C₄	C₂³×C₅	1	2	yes	—
314	C₄⋊C₄	C₂³×C₅	1	2	yes	—
315	C₄⋊C₄	C₂³×C₅	1	4	yes	—
316	C₄⋊C₄	C₂³×C₅	1	4	yes	—
317	C₄⋊C₄	C₂³×C₅	1	4	yes	—
318	C₄⋊C₄	C₂³×C₅	1	4	yes	—
319	C₄⋊C₄	C₂³×C₅	1	4	yes	—
320	C₄⋊C₄	C₂³×C₅	1	2	yes	—
321	C₄⋊C₄	C₂³×C₅	1	2	yes	—
322	C₄⋊C₄	C₂³×C₅	1	2	yes	—
323	C₄⋊C₄	C₂³×C₅	1	4	yes	—
324	C₄⋊C₄	C₂³×C₅	1	2	yes	—
325	C₄⋊C₄	C₂³×C₅	1	4	yes	—
326	C₄⋊C₄	C₂³×C₅	1	4	yes	—
327	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
328	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
329	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
330	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
331	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
332	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
333	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
334	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
335	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
336	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
337	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
338	C₄²	C₂³×C₅	1	1	yes	characteristic
339	C₄²	C₂³×C₅	1	1	yes	characteristic
340	C₄²	C₂³×C₅	1	1	yes	characteristic
341	C₄²	C₂³×C₅	1	1	yes	characteristic
342	C₄²	C₂³×C₅	1	4	yes	—
343	C₄²	C₂³×C₅	1	2	yes	—
344	C₄²	C₂³×C₅	1	2	yes	—
345	C₄²	C₂³×C₅	1	2	yes	—
346	C₄²	C₂³×C₅	1	4	yes	—
347	C₄²	C₂³×C₅	1	4	yes	—
348	C₄²	C₂³×C₅	1	4	yes	—
349	C₂×C₅	—	4	1	no	—
350	C₂×C₅	—	4	2	no	—
351	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
352	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
353	C₂×C₅	#585	1	1	yes	characteristic
354	C₂³	C₂⁴×C₅	1	1	yes	characteristic
355	C₂³	C₂⁴×C₅	1	2	yes	—
356	Q₈	—	2	2	no	—
357	Q₈	—	2	2	no	—
358	Q₈	—	2	2	no	—
359	Q₈	—	2	4	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	4	no	—
363	D₄	—	2	2	no	—
364	D₄	—	4	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
371	C₂×C₄	C₂⁴×C₅	1	4	yes	—
372	C₂×C₄	C₂⁴×C₅	1	2	yes	—
373	C₂×C₄	C₂⁴×C₅	1	2	yes	—
374	C₂×C₄	C₂⁴×C₅	1	2	yes	—
375	C₂×C₄	C₂⁴×C₅	1	2	yes	—
376	C₂×C₄	C₂⁴×C₅	1	2	yes	—
377	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
378	C₂×C₄	C₂⁴×C₅	1	2	yes	—
379	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
380	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
381	C₂×C₄	C₂⁴×C₅	1	4	yes	—
382	C₂×C₄	C₂⁴×C₅	1	2	yes	—
383	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
384	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
385	C₅	#3555	1	1	yes	characteristic, direct product factor, Sylow
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	1	no	—
392	C₂²	C₂⁵×C₅	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	4	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	4	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	C₅×2₋¹⁺⁴	1	2	yes	—
407	C₄	C₅×2₋¹⁺⁴	1	2	yes	—
408	C₂	—	4	1	no	—
409	C₂	—	4	2	no	—
410	C₂	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
411	C₂	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
412	C₂	C₅×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₅
prime radical	C₅×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅×#563	C₂	semidirect
2. C₅×Q₈²	C₂	semidirect
3. C₅×#557	C₂	semidirect
4. C₅×#557	C₂	semidirect
5. C₅×#556	C₂	semidirect
6. C₅×#556	C₂	semidirect
7. C₅×#556	C₂	semidirect
8. C₅×#554	C₂	semidirect
9. C₅×#552	C₂	semidirect
10. C₅×#544	C₂	semidirect
12. C₅×#541	C₂	semidirect
13. C₅×#541	C₂	semidirect
14. C₅×#541	C₂	semidirect
15. C₅×#533	C₂	semidirect
16. C₅×#533	C₂	semidirect
83. #3555	C₅	direct (N × H)
149. #563	C₂×C₅	semidirect
150. Q₈²	C₂×C₅	semidirect
151. #557	C₂×C₅	semidirect
152. #557	C₂×C₅	semidirect
153. #556	C₂×C₅	semidirect
154. #556	C₂×C₅	semidirect
155. #556	C₂×C₅	semidirect
156. #554	C₂×C₅	semidirect
157. #552	C₂×C₅	semidirect
158. #544	C₂×C₅	semidirect
160. #541	C₂×C₅	semidirect
161. #541	C₂×C₅	semidirect
162. #541	C₂×C₅	semidirect
163. #533	C₂×C₅	semidirect
164. #533	C₂×C₅	semidirect
385. C₅	#3555	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#563	2
C₅×Q₈²	2
C₅×#557	2
C₅×#556	2
C₅×#554	2
C₅×#552	2
C₅×#544	2
C₅×#542	2
C₅×#541	2
C₅×#533	2
C₅×#529	2
#3555	5

Subgroups — C5×#3555 #10619340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#3555 #10619340